new domain for atan() in Aug 8 draft.

[Michel Hack (1-914-784-7648) <hack@xxxxxxxxxxxxxx>]

The correctly-rounded domain was [-1/8, +1/8]; now it is [-inf,+inf].

Does this mean that atan() is now required to produce results whose
absolute value exceeds pi/2, for round-to-nearest binary32, and for
all formats with round-away-from-zero?

For reference, I show pi/2 in decimal, and in the three binary formats
expanded to show 64 additional fraction bits (so the machine format is
as if truncated towards zero).  The + and - signs show that rounding
to nearest would round up or down, respectively:

*       ....:.|..1....:|...2....:....3...|:....4
pi/2 = 1.57079632679489661923132169163975144209858469968755291...
*              -        +                 -
*          decimal32 decimal64        decimal128

binary32  pi/2 = 3FC90FDA                             A22168C2 34C4C662  +
binary64  pi/2 = 3FF921FB 54442D18                    469898CC 51701B83  -
binary128 pi/2 = 3FFF921F B54442D1 8469898C C51701B8  39A25204 9C1114D0  -

Michel.


Sent: 2006-08-13 00:39:12 UTC